28
votes
2answers
842 views

Schubert calculus, as lowbrow as possible

Starting in a week I'm going to be an instructor at a summer program for exceptionally mathematically talented high school students, and I'm going to be teaching a class on Schubert calculus. The ...
11
votes
2answers
647 views

Anything special (historical?) about surface $x\cdot y\cdot z\ +\ x+y+z=0$?

QUESTION I wanted to introduce and develop the complex logarithm from scratch. As the result I've arrived a couple of months ago at the following identity after which the road to complex logarithm is ...
43
votes
9answers
2k views

Taking “Zooming in on a point of a graph” seriously

In calculus classes it is sometimes said that the tangent line to a curve at a point is the line that we get by "zooming in" on that point with an infinitely powerful microscope. This explanation ...
80
votes
7answers
7k views

How to memorise (understand) Nakayama's lemma and its corollaries?

Hope this question is fine. Nakayama's lemma http://en.wikipedia.org/wiki/Nakayama_lemma#Statement is mentioned in the majority of books on algebraic geometry that treat varieties. So I think, I red ...
36
votes
11answers
4k views

Interesting results in algebraic geometry accessible to 3rd year undergraduates

On another thread I asked how I could encourage my final year undergraduate colleagues to take an algebraic geometry or complex analysis courses during their graduate studies. Willie Wong proposed me ...
5
votes
1answer
2k views

How would You encourage graduate students to learn algebraic geometry and/or complex analysis?

Hello, I am the 3rd year undegraduate student of mathematics. After I obtain a bachelor degree I want to study maths at graduate level, especially algebraic geometry and complex analysis. This fields ...
44
votes
4answers
2k views

What algorithm in algebraic geometry should I work on implementing?

This summer my wife and one of my friends (who are both programmers and undergraduate math majors, but have not learned any algebraic geometry) want to learn some algebraic geometry from me, and I ...
31
votes
4answers
2k views

Motivation for concepts in Algebraic Geometry

I know there was a question about good algebraic geometry books on here before, but it doesn't seem to address my specific concerns. ** Question ** Are there any well-motivated introductions to ...